Thermal energy problem: Gas expansion in cylinder

[Bonapartist]

Homework Statement

A vertical heat-insulated cylinder is divided into two parts by a movable piston of mass m. Initially, the piston is held at rest. The top part is evacuated and the bottom part is filled with 1 mol of monatomic gas at temperature 300 K. After the piston is released and the system comes to equilibrium, the volume occupied by the gas is halved. Find the final temperature of the gas.

Homework Equations

PV = nRT
S = Q/T
mg = PA?[/B]

The Attempt at a Solution

I've attempted to solve this problem using the fact that mg = PA and that the pressure can be solved for. Is this incorrect?

Thanks! As the first time I've posted on PF, I am delighted to be a contributing member!

 

[Riverbirdy]

Homework Statement

A vertical heat-insulated cylinder is divided into two parts by a movable piston of mass m. Initially, the piston is held at rest. The top part is evacuated and the bottom part is filled with 1 mol of monatomic gas at temperature 300 K. After the piston is released and the system comes to equilibrium, the volume occupied by the gas is halved. Find the final temperature of the gas.

Homework Equations

PV = nRT
S = Q/T
mg = PA?[/B]

The Attempt at a Solution

I've attempted to solve this problem using the fact that mg = PA and that the pressure can be solved for. Is this incorrect?

Thanks! As the first time I've posted on PF, I am delighted to be a contributing member!

Considering the process is adiabatic(ideally insulated q=0, no heat transfer involved in the process), use PV^k=const or P₁V₁^k=P₂V₂^k
k is just the heat capacity ratio of the gas given k=C_p/C_v

 

[Bonapartist]

I've solved it to be 476.22 K, a reasonable answer. Thanks for pointing out its adiabatic nature!

 

[Riverbirdy]

I've solved it to be 476.22 K, a reasonable answer. Thanks for pointing out its adiabatic nature!

Your welcome.